Here is a place to start for you. Looking at the picture (a picture is worth 1000 words), your PLC would need to include the following Inputs and Outputs.
1. An encoder input for the Carriage Drive Motor Position for the cutting cart that is mounted on tracks with a toothed tracking wheel, because "The cutter cuts the length in a controlled manner...".
2. Digital inputs for the following:
System Start N.O. Pushbutton,
System Stop N.C. Pushbutton,
Bar End Stop Limit Switch,
Torch Flame Detector Input,
and 2 limit switch Inputs for each of the following because "they are fitted with position sensors to signal their movements":
Carriage Cutter Transverse Cylinder Out and In limit switches,
Bar Pusher Cylinder Out and In limit switches,
Bar Clamp Cylinder Up and Down Limit Switches,
Bar Ejector Rotary Actuator Travel limit switches.
3. Digital Outputs for the following because "All the actuators are hydraulic and controlled by electric solenoid valves,":
Green System Run Indicator Light,
Torch Flame Igniter Output
Carriage Traverse Cylinder Out and In Solenoid Outputs,
Carriage Drive Motor Forward and Reverse Solenoid Outputs,
Bar Pusher Cylinder Out and In Solenoid Outputs,
Bar Clamp Cylinder Up and Down Solenoid Outputs,
Bar Ejector Rotary Actuator Out and In Solenoid Outputs.
Now find a mid-range modular PLC that has module slots and I/O modules for the above Inputs and Outputs.
